Results 1 to 10 of about 39 (37)
Arithmetic matroids and Tutte polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce the notion of arithmetic matroid, whose main example is provided by a list of elements in a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a ...
Michele D'Adderio, Luca Moci
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Splines, lattice points, and (arithmetic) matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Let $X$ be a $(d \times N)$-matrix. We consider the variable polytope $\Pi_X(u) = \left\{ w \geq 0 : Xw = u \right\}$. It is known that the function $T_X$ that assigns to a parameter $u \in \mathbb{R}^N$ the volume of the polytope $\Pi_X(u)$ is piecewise
Matthias Lenz
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Representations of torsion-free arithmetic matroids [PDF]
European Journal of Combinatorics, 2021 We study the representability problem for torsion-free arithmetic matroids. By using a new operation called "reduction" and a "signed Hermite normal form", we provide and implement an algorithm to compute all the representations, up to equivalence. As an application, we disprove two conjectures about the poset of layers and the independence poset of a ...
Pagaria, Roberto, Paolini, Giovanni
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The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids [PDF]
Journal of Algebra, 2021 Final version, to appear on Journal of ...
Bruns W., Garcia-Sanchez P. A., Moci L.
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Rectilinear approximation and volume estimates for hereditary bodies via [0, 1]‐decorated containers
Journal of Graph Theory, Volume 104, Issue 1, Page 104-132, September 2023., 2023 Abstract We use the hypergraph container theory of Balogh–Morris–Samotij and Saxton–Thomason to obtain general rectilinear approximations and volume estimates for sequences of bodies closed under certain families of projections. We give a number of applications of our results, including a multicolour generalisation of a theorem of Hatami, Janson and ...
Victor Falgas‐Ravry +3 more
wiley +1 more source
The multivariate arithmetic Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two.
Petter Brändèn, Luca Moci
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On generalisations of the Aharoni–Pouzet base exchange theorem
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1540-1549, June 2023., 2023 Abstract The Greene–Magnanti theorem states that if M$ M$ is a finite matroid, B0$ B_0$ and B1$ B_1$ are bases and B0=⋃i=1nXi$ B_0=\bigcup _{i=1}^{n} X_i$ is a partition, then there is a partition B1=⋃i=1nYi$ B_1=\bigcup _{i=1}^{n}Y_i$ such that (B0∖Xi)∪Yi$ (B_0 \setminus X_i) \cup Y_i$ is a base for every i$ i$. The special case where each Xi$ X_i$ is
Zsuzsanna Jankó, Attila Joó
wiley +1 more source
On the cohomology of arrangements of subtori
Journal of the London Mathematical Society, Volume 106, Issue 3, Page 1999-2029, October 2022., 2022 Abstract Given an arrangement of subtori of arbitrary codimension in a complex torus, we compute the cohomology groups of the complement. Then, by using the Leray spectral sequence, we describe the multiplicative structure on the associated graded cohomology. We also provide a differential model for the cohomology ring, by considering a toric wonderful
Luca Moci, Roberto Pagaria
wiley +1 more source
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids.
Alex Fink, Luca Moci
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Orientable arithmetic matroids [PDF]
Discrete Mathematics, 2020 13 pages, 1 ...
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